Stochastic modeling of suspended sediment transport in regular and extreme flow environments
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Transport of sediments creates a variety of environmental impacts because it not only induces erosion and deposition problems, but also transfers contaminants or viruses adhered or coupled with the sediments. A better understanding of the fundamental sediment transport processes is significant for environmental researchers to provide practical and scientifically sound solutions to hydraulic engineering problems. Stochastic characteristics of sediment transport have been identified from experiment data. The trajectory of a sediment particle is stochastic due to the probabilistic nature of the flow and sediment conditions. The main goal of the study is to develop a stochastic model governing suspended sediment transport. In this research, several issues related to stochastic modelling of suspended sediment transport are discussed: the numerical scheme for the Fokker-Planck equation; suspended sediment transport in regular surface flows; and suspended sediment transport in extreme flow environments. A fourth-order accurate numerical scheme has been developed for the two-dimensional advection-diffusion (A-D) equation in a staggered-grid system. The first-order spatial derivatives are approximated by the fourth-order accurate finite-difference scheme, thus all truncation errors are kept to a smaller order of magnitude than those of the diffusion terms. For the time derivative, the fourth-order accurate Adams-Bashforth predictor-corrector method is applied. The stability analysis of the proposed scheme is carried out using the Von Neumann method. It is shown that the proposed algorithm has good stability. The proposed numerical scheme can provide more accurate results for long-time simulations validated against analytical and/or numerical solutions. A stochastic partial differential equation based model has been derived based on the law of conservation of mass and the Langevin equation of particle displacement to simulate suspended sediment transport in open-channel flows. The proposed model, explicitly expressing the randomness of sediment concentrations, has the advantage of capturing an instantaneous profile of sediment concentrations including not only the mean but also the variance compared with the deterministic A-D equation. As a result, the probability distribution of the sediment transport rate can be characterized based on a number of realizations obtained in the numerical experiments. The lattice approximation is applied to solve the SPDE of suspended sediment transport in open channel flow. The ensemble mean sediment concentration of the proposed SPDE, obtained by the Monte Carlo simulation, agrees well with that of the deterministic A-D equation. This study proposed a stochastic jump diffusion model in response to extreme flows to describe the movement of sediment particles in surface waters. The proposed approach classifies the movement of particles into three categories - a drift motion, a Brownian type motion due to turbulence in the flow field for example, and jumps due to occurrence of extreme events. In the proposed stochastic diffusion jump model, the occurrence of the extreme flow events is modeled as a Poisson process. The frequency of occurrence of the extreme events in the stochastic diffusion jump model can be explicitly accounted for in the evaluation of movement of sediment particles. The ensemble mean and variance of particle trajectory can be obtained from the proposed model. As such, the stochastic diffusion jump model, when coupled with an appropriate hydrodynamic model, can assist in developing a forecast model to predict the movement of particles in the presence of extreme flows.